A renegade Libyan general launched an offensive on Sunday against Islamist militants in the eastern city of Benghazi, prompting dozens of families to flee the port in the latest bout of turmoil to hit the North African oil-producing nation.

Meanwhile, power has gone off in much of eastern Libya after a power plant in Benghazi was shelled in heavy clashes in the port city, a state electricity official said.

"The clashes in Benghazi have caused a big lack of power in the east of Libya," said Lutfi Ghuma, spokesman for Libya's state electricity company. "The circuits ... of the Benghazi North Power Station have been damaged because of the shelling, causing power cuts in most of the eastern cities of Libya and some other western areas."

Engineers were trying to fix the damage but they were facing difficulties to reach the damaged plant, he said.

Libyan authorities are struggling to restore order across the vast desert nation ahead of a June 25 parliamentary election. The situation remains especially chaotic in Benghazi, Libya's second largest city and cradle of the Nato-backed uprising that toppled Muammar Gaddafi three years ago.

Retired general Khalifa Haftar has declared war against militants in Benghazi and several army units have joined him, though the Tripoli government says he has no authority to act.

"There are now heavy clashes in Sidi Faraj and al-Hawari (in western Benghazi). Our forces are attacking with tanks and rocket launchers," Haftar's spokesman Mohamed El Hejazi said.

Residents were seen packing belongings into cars and heading out of the area to escape the fighting.

Hejazi said Haftar had warned the Islamists against shipping in arms via the commercial port of Derna, east of Benghazi.

Derna is a hotspot for Ansar Al-Sharia and other militant groups amid Libya's persistent power vacuum. The US designates Ansar Al-Sharia a terrorist organisation.

Haftar was once close to Gaddafi but fell out with him and then played a role in the 2011 uprising. In February, he stirred rumours of a coup by appearing in military uniform to call for a presidential committee to be formed to govern till an election.

Libya's government and parliament are paralysed by divisions between Islamists and more moderate forces as well as competing tribes and regions. - Reuters